Solve x^2-x+7/x=f(x)

$$\frac { x ^ { 2 } - x + 7 } { x } = f ( x )$$

Solve for f

$$f=\frac{x^{2}-x+7}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x^{2}-x+7=fxx$$

Multiply x and x to get x^{2}.

$$x^{2}-x+7=fx^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$fx^{2}=x^{2}-x+7$$

The equation is in standard form.

$$x^{2}f=x^{2}-x+7$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{x^{2}-x+7}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$f=\frac{x^{2}-x+7}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{28f-27}+1}{2\left(1-f\right)}\text{; }x=\frac{-\sqrt{28f-27}+1}{2\left(1-f\right)}\text{, }&f\neq 1\\x=7\text{, }&f=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{28f-27}+1}{2\left(1-f\right)}\text{; }x=\frac{-\sqrt{28f-27}+1}{2\left(1-f\right)}\text{, }&f\neq 1\text{ and }f\geq \frac{27}{28}\\x=7\text{, }&f=1\end{matrix}\right.$$